arXiv subjects

Alexander Zuyev

Publications and source records attributed to Alexander Zuyev.

41 records · Page 3Linked to original sources

arXiv2018

Modal approach to the controllability problem of distributed parameter systems with damping

This paper is devoted to the controllability analysis of a class of linear control systems in a Hilbert space. It is proposed to use the minimum energy controls of a reduced lumped parameter system for solving the infinite dimensional steering problem approximately. Sufficient conditions of the approximate controllability are formulated for a modal representation of a flexible structure with small damping.

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arXiv2018

A family of extremum seeking laws for a unicycle model with a moving target: theoretical and experimental studies

In this paper, we propose and practically evaluate a class of gradient-free control functions ensuring the motion of a unicycle-type system towards the extremum point of a time-varying cost function. We prove that the unicycle is able to track the extremum point, and illustrate our results by numerical simulations and experiments that show that the proposed control functions exhibit an improved tracking performance in comparison to standard extremum seeking laws based on Lie bracket approximations.

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arXiv2018

Modeling and stabilization of a rotating mechanical system with elastic plates

A mechanical system consisting of a rigid body and attached Kirchhoff plates under the action of three independent controls torques is considered. The equations of motion of such model are derived in the form of a system of coupled nonlinear ordinary and partial differential equations. The operator form of this system is represented as an abstract differential equation in a Hilbert space. A feedback control law is constructed such that the corresponding infinitesimal generator is dissipative.

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arXiv2017

On a class of generating vector fields for the extremum seeking problem: Lie bracket approximation and stability properties

In this paper, we describe a broad class of control functions for extremum seeking problems. We show that it unifies and generalizes existing extremum seeking strategies which are based on Lie bracket approximations, and allows to design new controls with favorable properties in extremum seeking and vibrational stabilization tasks. The second result of this paper is a novel approach for studying the asymptotic behavior of extremum seeking systems. It provides a constructive procedure for defining frequencies of control functions to ensure the practical asymptotic and exponential stability. In contrast to many known results, we also prove asymptotic and exponential stability in the sense of Lyapunov for the proposed class of extremum seeking systems under appropriate assumptions on the vector fields.

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arXiv2015

Exponential Stabilization of Nonholonomic Systems by means of Oscillating Controls

This paper is devoted to the stabilization problem for nonlinear driftless control systems by means of a time-varying feedback control. It is assumed that the vector fields of the system together with their first order Lie brackets span the whole tangent space at the equilibrium. A family of trigonometric open-loop controls is constructed to approximate the gradient flow associated with a Lyapunov function. These controls are applied for the derivation of a time-varying feedback law under the sampling strategy. By using Lyapunov's direct method, we prove that the controller proposed ensures exponential stability of the equilibrium. As an example, this control design procedure is applied to stabilize the Brockett integrator.

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